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GR9277 #13
Problem
 GREPhysics.NET Official Solution Alternate Solutions
\prob{13}
Listed below are Maxwell's equations of electromagnetism. If magnetic monopoles exist, which of these equations would be INCORRECT?
I. Curl $\vec{H}=\vec{J}+\partial_t \vec{D}$
II. Curl $\vec{H}=\vec{J}+\partial_t \vec{D}$
III. Curl $\vec{H}=\vec{J}+\partial_t \vec{D}$
IV. Curl $\vec{H}=\vec{J}+\partial_t \vec{D}$

1. IV only
2. I and II
3. I and III
4. II and IV
5. III and IV

Electromagnetism$\Rightarrow$}Maxwell's Equations

Magnetic monopoles remain a likeable (even lovable) theoretical construct because of their ability to perfectly symmetrize Maxwell's equations. Since the curl term has an electric current, the other curl term should have a magnetic current. ($\nabla \cdot B \neq 0$ is taken to be obvious in presence of magnetic charge.) The answer is thus (D), and the revised equations are,

$\begin{eqnarray} \nabla \times H = J_e+\frac{\partial D}{\partial t}\\ \nabla \times E = -J_m-\frac{\partial B}{\partial t}\\ \nabla \cdot D = \rho_e\\ \nabla \cdot B = \rho_m.
\end{eqnarray}$

Alternate Solutions
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2018-12-14 00:44:47
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techblaster
2018-08-19 15:46:08
solidstate
2011-10-24 21:11:18
Isn't there TYPO in the question???
ramparts
2009-08-09 17:13:54
Even if you don't know exactly how the equations would change with monopoles, if you know that monopoles symmetrize the equations (by making some terms not 0), just compare like equations and see which ones are missing pieces. Eqn II is like Eqn I but without the J, and Eqn IV is like Eqn III but without the rho.
hoyas08
2007-12-26 16:45:26
The choices should be:

I. Curl H = J + ∂D/∂t
II. Curl E = -∂B/∂t
III. div D = ρ
IV. div B = 0

I think the answer is still D with these choices.
bootstrap
2007-04-05 19:14:29
All 4 of the curls in the question are exactly the same.
bootstrap
2007-04-05 19:14:20
All 4 of the curls in the question are exactly the same.
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